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Number of ways to place n nonattacking composite pieces rook + rider[3,4] on an n X n chessboard.
1

%I #8 Apr 21 2021 13:44:34

%S 1,2,6,24,80,326,1566,9544,53696,347382,2566892,21907934,184868860,

%T 1704360992,17294597926,192725663600,2139133978996

%N Number of ways to place n nonattacking composite pieces rook + rider[3,4] on an n X n chessboard.

%C a(n) is also number of permutations p of 1,2,...,n satisfying |p(i+3k)-p(i)|<>4k AND |p(j+4k)-p(j)|<>3k for all i>=1, j>=1, k>=1, i+3k<=n, j+4k<=n.

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens, kings, bishops and knights</a> (in English and Czech)

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fairy_chess_piece">Fairy chess piece</a>

%Y Cf. A000170, A189851, A189855.

%K nonn,hard

%O 1,2

%A _Vaclav Kotesovec_, Apr 29 2011